#This script contributed to Figure 1 of the manuscript submitted to
#Philosophical Transactions of the Royal Society B on July 14, 2017
#Authors: Civitello DJ, Allman BE, Morozumi C, and Rohr JR.
#Title: "Fertilization, eutrophication, and food provisioning: an integrative view of resource supplementation and wildlife disease dynamics."

setwd("P:/RData")

library(deSolve)

#####
#SIZR
#####

#definition of SIZR model
disease.web.SIZR <- function(t,y,params){
  S = y[1]; I = y[2]; Z = y[3]; R = y[4]; #reference initial conditions
  with(
    as.list(params),
    {
      dS <- e.S*f.S*(S + I)*R - d*S - u*f.S*S*Z # primary host dynamics dynamics
      
      dI <- u*f.S*S*Z - (d+v)*I # Infected primary host dynamics
      
      dZ <- sigma*(R/(R+Rh))*(d+v)*I - m*Z - f.S*(S+I)*Z # Parasite dynamics
      
      dR <- r*R*(1 - R/K) - f.S*(S+I)*R # Resource dynamics
      
      res <- c(dS, dI, dZ, dR) #store results
      list(res)
    }
  )
}

#Run model to equilibrium for a set of r values
times = seq(from=1, to=4000, by=1)
outSIZR = matrix(nrow=0, ncol=4)
r.set = (1:100)/100

for(i in 1:length(r.set)){
  
  #Specification of model parameters
  params = c(e.S=0.5, f.S=0.01, f.P=0.0002, d=0.05, d.P=0.01, 
             u=1e-4, v=0.05, e.C=0.5, f.C=0.0075, 
             sigma=1e5, Rh=20, m=0.2, r=r.set[i], K=250)
  xstart = c(S = 10, I = 0, Z = 100, R=250)
  #run model and store equilibrium values of each player in the model
  outSIZR = rbind(outSIZR, as.data.frame(lsoda(xstart, times, disease.web.SIZR, params))[length(times),])
}

#calculate prevalence
prev = outSIZR$I/(outSIZR$I + outSIZR$S)

plot(r.set, prev, type="l")

write.table(outSIZR, file="outSIZR.csv")


#####
#SIZRC
#####

#definition of SIZRC model
disease.web.SIZRC <- function(t,y,params){
  S = y[1]; I = y[2]; Z = y[3]; R = y[4]; C = y[5];#reference initial conditions
  with(
    as.list(params),
    {
      dS <- e.S*f.S*(S + I)*R - d*S - u*f.S*S*Z # primary host dynamics
      
      dI <- u*f.S*S*Z - (d+v)*I # Infected primary host dynamics
      
      dZ <- sigma*(R/(R+Rh))*(d+v)*I - m*Z - f.S*(S+I)*Z - f.C*C*Z # Parasite dynamics
      
      dR <- r*R*(1 - R/K) - f.S*(S+I)*R -f.C*C*R # Resource dynamics
      
      dC <- e.C*f.C*C*R - d*C # Competitor dynamics
      
      res <- c(dS, dI, dZ, dR, dC) #store results
      list(res)
    }
  )
}

#Run model to equilibrium for a set of r values
times = seq(from=1, to=4000, by=1)
outSIZRC = matrix(nrow=0, ncol=5)
r.set = (1:100)/100
xstart = c(S = 10, I = 0, Z = 100, R=250, C=10)
for(i in 1:length(r.set)){
  
  #Specification of model parameters
  params = c(e.S=0.5, f.S=0.01, f.P=0.0002, d=0.05, d.P=0.01, 
             u=1e-4, v=0.05, e.C=0.5, f.C=0.0075, 
             sigma=1e5, Rh=20, m=0.2, r=r.set[i], K=250)
  #run model and store equilibrium values of each player in the model
  outSIZRC = rbind(outSIZRC, as.data.frame(lsoda(xstart, times, disease.web.SIZRC, params))[length(times),])
}

#calculate prevalence
prev = outSIZRC$I/(outSIZRC$I + outSIZRC$S)

plot(r.set, prev, type="l")
write.table(outSIZRC, file="outSIZRC.csv")

#####
#SIZRP
#####

#definition of SIZRP model
disease.web.SIZRP <- function(t,y,params){
  S = y[1]; I = y[2]; Z = y[3]; R = y[4]; P = y[5];#reference initial conditions
  with(
    as.list(params),
    {
      dS <- e.S*f.S*(S + I)*R - d*S - u*f.S*S*Z - f.P*P*S # primary host dynamics
      
      dI <- u*f.S*S*Z - (d+v)*I - f.P*P*I # Infected primary host dynamics
      
      dZ <- sigma*(R/(R+Rh))*(d+v)*I - m*Z - f.S*(S+I)*Z # Parasite dynamics
      
      dR <- r*R*(1 - R/K) - f.S*(S+I)*R # Resource dynamics
      
      dP <- f.P*(S + I)*P - d.P*P # Predator dynamics
      
      res <- c(dS, dI, dZ, dR, dP) #store results
      list(res)
    }
  )
}

#Run model to equilibrium for a set of r values
times = seq(from=1, to=4000, by=1)
outSIZRP = matrix(nrow=0, ncol=5)
r.set = (1:100)/100

for(i in 1:length(r.set)){
  
  #Specification of model parameters
  params = c(e.S=0.5, f.S=0.01, f.P=0.0002, d=0.05, d.P=0.01, 
             u=1e-4, v=0.05, e.C=0.5, f.C=0.0075, 
             sigma=1e5, Rh=20, m=0.2, r=r.set[i], 
             K=250)
  xstart = c(S = 10, I = 0, Z = 100, R=250, P=10)
  #run model and store equilibrium values of each player in the model
  outSIZRP = rbind(outSIZRP, as.data.frame(lsoda(xstart, times, disease.web.SIZRP, params))[length(times),])
}

#calculate prevalence
prev = outSIZRP$I/(outSIZRP$I + outSIZRP$S)

plot(r.set, prev, type="l")
write.table(outSIZRP, file="outSIZRP.csv")

#####
#SIZRCP
#####

#definition of SIZRCP model
disease.web.SICZRP <- function(t,y,params){
  S = y[1]; I = y[2]; C = y[3]; Z = y[4]; R = y[5]; P= y[6];#reference initial conditions
  with(
    as.list(params),
    {
      dS <- e.S*f.S*(S + I)*R - d*S - u*f.S*S*Z - f.P*P*S # primary host dynamics
      
      dI <- u*f.S*S*Z - (d+v)*I - f.P*P*I # Infected primary host dynamics
      
      dC <- e.C*f.C*C*R - d*C - f.P*P*C # Competitor dynamics
      
      dZ <- sigma*(R/(R+Rh))*(d+v)*I - m*Z - (f.S*(S+I) + f.C*C)*Z # Parasite dynamics
      
      dR <- r*R*(1 - R/K) - (f.S*(S+I) + f.C*C)*R # Resource dynamics
      
      dP <- f.P*(S + I + C)*P - d.P*P # Predator dynamics
      
      res <- c(dS, dI, dC, dZ, dR, dP) #store results
      list(res)
    }
  )
}

#Run model to equilibrium for a set of r values
times = seq(from=1, to=4000, by=1)
outSICZRP = matrix(nrow=0, ncol=6)
r.set = (1:100)/100

for(i in 1:length(r.set)){
  
  #Specification of model parameters
  params = c(e.S=0.5, f.S=0.01, f.P=0.0002, d=0.05, d.P=0.01, 
             u=1e-4, v=0.05, e.C=0.5, f.C=0.0075, 
             sigma=1e5, Rh=20, m=0.2, r=r.set[i], K=250)
  
  xstart = c(S = 10, I = 0, C=10, Z = 100, R=250, P=10)
  #run model and store equilibrium values of each player in the model
  outSICZRP = rbind(outSICZRP, as.data.frame(lsoda(xstart, times, disease.web.SICZRP, params))[length(times),])
}

#calculate prevalence
prev = outSICZRP$I/(outSICZRP$I + outSICZRP$S)

plot(r.set, prev, type="l")
write.table(outSICZRP, file="outSICZRP.csv")